Problem: Reduce to lowest terms: $- \dfrac{3}{2} \div - \dfrac{1}{6} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{1}{6}$ is $- \dfrac{6}{1}$ Therefore: $ - \dfrac{3}{2} \div - \dfrac{1}{6} = - \dfrac{3}{2} \times - \dfrac{6}{1} $ $ \phantom{- \dfrac{3}{2} \times - \dfrac{6}{1}} = \dfrac{-3 \times -6}{2 \times 1} $ $ \phantom{- \dfrac{3}{2} \times - \dfrac{6}{1}} = \dfrac{18}{2} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{18}{2} = \dfrac{18 \div 2}{2 \div 2} = 9 $